Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
416 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22589949 | C2 | semidirect |
| 3. #22588368 | C2 | semidirect |
| 4. #22586352 | C2 | semidirect |
| 5. #22586350 | C2 | semidirect |
| 6. #22586348 | C2 | semidirect |
| 7. C71×#1348 | C2 | semidirect |
| 8. C2×#14556151 | C4 | semidirect |
| 12. #17986237 | C4 | semidirect |
| 13. #17986236 | C4 | semidirect |
| 17. #17986036 | C4 | semidirect |
| 195. #1348 | D71 | semidirect |
| 198. C71 | #11890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597923 | 2 |
| #22589949 | 2 |
| #22588368 | 2 |
| #22586352 | 2 |
| #22586350 | 2 |
| #22586348 | 2 |
| C71×#1348 | 2 |
| #11890 | 71 |